Question: Simplify the following expression: $\dfrac{56z^4}{77z^2}$ You can assume $z \neq 0$.
$ \dfrac{56z^4}{77z^2} = \dfrac{56}{77} \cdot \dfrac{z^4}{z^2} $ To simplify $\frac{56}{77}$ , find the greatest common factor (GCD) of $56$ and $77$ $56 = 2 \cdot 2 \cdot 2 \cdot 7$ $77 = 7 \cdot 11$ $ \mbox{GCD}(56, 77) = 7 $ $ \dfrac{56}{77} \cdot \dfrac{z^4}{z^2} = \dfrac{7 \cdot 8}{7 \cdot 11} \cdot \dfrac{z^4}{z^2} $ $\phantom{ \dfrac{56}{77} \cdot \dfrac{4}{2}} = \dfrac{8}{11} \cdot \dfrac{z^4}{z^2} $ $ \dfrac{z^4}{z^2} = \dfrac{z \cdot z \cdot z \cdot z}{z \cdot z} = z^2 $ $ \dfrac{8}{11} \cdot z^2 = \dfrac{8z^2}{11} $